Revenue Maximization Under Unknown Private Values with Non-Obligatory Inspection

38 Pages Posted: 5 Jun 2021 Last revised: 4 Oct 2021

See all articles by Saeed Alaei

Saeed Alaei

affiliation not provided to SSRN

Ali Makhdoumi

Fuqua School of Business; Massachusetts Institute of Technology (MIT)

Azarakhsh Malekian

University of Toronto - Rotman School of Management; Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science

Date Written: May 28, 2021

Abstract

We consider the problem of selling a single item to $n$ unit-demand buyers to maximize revenue, where the buyers' values are independently distributed (not necessarily identical) according to publicly known distributions but unknown to the buyers themselves, with the option of allowing buyers to inspect the item at a cost. This problem can be interpreted as a revenue-maximizing variant of Weitzman's Pandora's problem with non-obligatory inspection. We present an approximation mechanism that achieves $1/2$. The proposed mechanism generalizes to the case of selling $k$ units of an item to unit-demand buyers, obtaining $1-1/\sqrt{k+3}$ of the optimal revenue in expectation. The mechanism is sequential and has a simple implementation that works in an online setting where buyers arrive in an arbitrary unknown order, yet achieving the aforementioned approximation with respect to the optimal offline mechanism.

Suggested Citation

Alaei, Saeed and Makhdoumi, Ali and Malekian, Azarakhsh, Revenue Maximization Under Unknown Private Values with Non-Obligatory Inspection (May 28, 2021). Rotman School of Management Working Paper No. 3855810, Available at SSRN: https://ssrn.com/abstract=3855810 or http://dx.doi.org/10.2139/ssrn.3855810

Saeed Alaei

affiliation not provided to SSRN

Ali Makhdoumi (Contact Author)

Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

HOME PAGE: http://https://www.fuqua.duke.edu/faculty/ali-makhdoumi

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Azarakhsh Malekian

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States

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